Characteristic Polynomials of Skew-Adjacency Matrices of Oriented Graphs

An oriented graph Gσ is a simple undirected graph G with an orientation, which assigns to each edge a direction so that Gσ becomes a directed graph. G is called the underlying graph of Gσ and we denote by S(Gσ) the skew-adjacency matrix of Gσ and its spectrum Sp(Gσ) is called the skew-spectrum of Gσ. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix S(Gσ) are given in terms of Gσ and as its applications, new combinatorial proofs of known results are obtained and new families of oriented bipartite graphs Gσ with Sp(Gσ) = iSp(G) are given.